2014 UNCO Math Contest II Problems/Problem 9

Problem

In the Queen’s croquet, as described in Problem $8$ , what is the probability that the ball hits the goal post the $n$ th time the ball is hit?

Zero probability for $n=1$ and $\frac{F_{n-1}}{2^{2n}}$ for $n\ge 2$ , where $F_{n-1}$ is the $(n-1)^{st}$ Fibonacci number.

2014 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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All UNCO Math Contest Problems and Solutions